By Thomas Ernst

To date, the theoretical improvement of q-calculus has rested on a non-uniform foundation. regularly, the cumbersome Gasper-Rahman notation was once used, however the released works on q-calculus regarded various reckoning on the place and by way of whom they have been written. This confusion of tongues not just advanced the theoretical improvement but additionally contributed to q-calculus ultimate a overlooked mathematical box. This booklet overcomes those difficulties through introducing a brand new and engaging notation for q-calculus in response to logarithms.For example, q-hypergeometric services are actually visually transparent and simple to track again to their hypergeometric mom and dad. With this new notation it's also effortless to work out the relationship among q-hypergeometric capabilities and the q-gamma functionality, anything that beforehand has been overlooked.

The publication covers many themes on q-calculus, together with certain services, combinatorics, and q-difference equations. except an intensive assessment of the ancient improvement of q-calculus, this ebook additionally provides the domain names of contemporary physics for which q-calculus is acceptable, comparable to particle physics and supersymmetry, to call only a few.

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### A Comprehensive Treatment of q-Calculus by Thomas Ernst

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